Reservoir crowding in a far-from-equilibrium exclusion process with dynamic defects

The transport phenomena frequently happen in many systems at all scales; be it the micro level such as the intracellular transport in biological systems or the macro level which includes vehicular traffic, pedestrian flow, etc. These physical systems exhibit complex behavior and violate the law of detailed balance under a stationary state. These processes are classified as driven-diffusive systems, driven by some external field or self-driven, and eventually reveal a non-equilibrium steady state having a distinctive non-zero current. In the last few decades, the totally asymmetrically simple exclusion process (TASEP) is found to be a classical model that provides a unified framework to analyze the collective properties of these stochastic transport problems. TASEP is a 1D lattice comprised of particles that hop stochastically and uni-directionally along the linear track following the hard-core exclusion principle.

Motivated by the biological process of gene transcription, we investigate a totally asymmetric simple exclusion process equipped with randomly distributed inhomogeneities “defects” that stochastically bind and unbind from the lattice with boundaries connected to a common reservoir. The total number of particles and defects in the system is conserved and controlled by the filling factor μ. Additionally, crowding of the reservoir is taken into account which regulates the entry and exit of particles from both boundaries as well as the binding and unbinding of defects. In the framework of mean-field approximation, we express the stationary state characteristics like density profiles and obtain the phase diagrams in α - β parameter space. In a novel simplification, we examine the effect of various parameters influencing the defect dynamics via a unifying parameter called the obstruction factor. Further, we elucidate the variation of the phase diagram with respect to the filling factor and obstruction factor. By examining the limiting values of the obstruction factor, its consequences have been carefully investigated on the phase boundaries. The theoretical findings are validated through extensive Monte Carlo simulations.